Regarded as an instant classic, probably one of the most popular titles amongst the classics. Not only will this be a fun book to read but a great book to discuss.

The Strange Case of Dr. Jekyll and Mr.Hyde
The Strange Case of Dr. Jekyll and Mr.Hyde dramatically brings to life a science-fiction case study of the nature of good and evil and the duality that can exist within one person. Resonant with psychological perception and ethical insight, the book has literary roots in Dostoevsky’s “The Double” and Crime and Punishment.

My own definition of a "classic" is something that is, beside being at least a certain age, also widely read and translated, and I think it's a bit too obscure in that respect. Perhaps it's an english-laguage classic, and my focus is more international...

In her most playful and exuberant novel, Virginia Woolf writes the "historical biography" of Orlando, a young boy of nobility during the reign of Queen Elizabeth I. A wild ride through four centuries, the novel shows Orlando aging, magically, only thirty-six years between 1588 and 1928. Even more magically, he also changes from a man to a woman.

Orlando enters the book as an Elizabethan nobleman and leaves the book three centuries later as a liberated woman of the 1920s. Along the way this most rambunctious of Woolf's characters engages in sword fights, trades barbs with 18th century wits, has a baby, and drives a car. As she explores Orlando's life, Woolf also explores the differing roles of men and women in society during various periods.

On the subject of Flatland, I would say that it's more a math classic than anything else. I think that Phosophical Investigations by Wittgenstein is doubtless a great classic, but I'm not going to nominate it; I think it's not appropriate.